Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group
This paper is devoted to the weak and strong estimates for the linear and multilinear fractional Hausdorff operators on the Heisenberg group Hn{{\mathbb{H}}}^{n}. A sharp strong estimate for TΦm{T}_{\Phi }^{m} is obtained. As an application, we derive the sharp constant for the product Hardy operato...
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De Gruyter
2021
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oai:doaj.org-article:738fb1d41eae4d17ba199fe5595620a42021-12-05T14:10:52ZWeak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group2391-545510.1515/math-2021-0016https://doaj.org/article/738fb1d41eae4d17ba199fe5595620a42021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0016https://doaj.org/toc/2391-5455This paper is devoted to the weak and strong estimates for the linear and multilinear fractional Hausdorff operators on the Heisenberg group Hn{{\mathbb{H}}}^{n}. A sharp strong estimate for TΦm{T}_{\Phi }^{m} is obtained. As an application, we derive the sharp constant for the product Hardy operator on Hn{{\mathbb{H}}}^{n}. Some weak-type (p,q)\left(p,q) (1≤p≤∞)\left(1\le p\le \infty ) estimates for TΦ,β{T}_{\Phi ,\beta } are also obtained. As applications, we calculate some sharp weak constants for the fractional Hausdorff operator on the Heisenberg group. Besides, we give an explicit weak estimate for TΦ,β→m{T}_{\Phi ,\overrightarrow{\beta }}^{m} under some mild assumptions on Φ\Phi . We extend the results of Guo et al. [Hausdorff operators on the Heisenberg group, Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 11, 1703–1714] to the fractional setting.Deng YangkendiZhang XingsongYan DunyanWei MingquanDe Gruyterarticlehausdorff operatorheisenberg groupmultilinearsharp bound42b2042b35MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 316-328 (2021) |
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DOAJ |
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hausdorff operator heisenberg group multilinear sharp bound 42b20 42b35 Mathematics QA1-939 |
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hausdorff operator heisenberg group multilinear sharp bound 42b20 42b35 Mathematics QA1-939 Deng Yangkendi Zhang Xingsong Yan Dunyan Wei Mingquan Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group |
| description |
This paper is devoted to the weak and strong estimates for the linear and multilinear fractional Hausdorff operators on the Heisenberg group Hn{{\mathbb{H}}}^{n}. A sharp strong estimate for TΦm{T}_{\Phi }^{m} is obtained. As an application, we derive the sharp constant for the product Hardy operator on Hn{{\mathbb{H}}}^{n}. Some weak-type (p,q)\left(p,q)
(1≤p≤∞)\left(1\le p\le \infty ) estimates for TΦ,β{T}_{\Phi ,\beta } are also obtained. As applications, we calculate some sharp weak constants for the fractional Hausdorff operator on the Heisenberg group. Besides, we give an explicit weak estimate for TΦ,β→m{T}_{\Phi ,\overrightarrow{\beta }}^{m} under some mild assumptions on Φ\Phi . We extend the results of Guo et al. [Hausdorff operators on the Heisenberg group, Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 11, 1703–1714] to the fractional setting. |
| format |
article |
| author |
Deng Yangkendi Zhang Xingsong Yan Dunyan Wei Mingquan |
| author_facet |
Deng Yangkendi Zhang Xingsong Yan Dunyan Wei Mingquan |
| author_sort |
Deng Yangkendi |
| title |
Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group |
| title_short |
Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group |
| title_full |
Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group |
| title_fullStr |
Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group |
| title_full_unstemmed |
Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group |
| title_sort |
weak and strong estimates for linear and multilinear fractional hausdorff operators on the heisenberg group |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/738fb1d41eae4d17ba199fe5595620a4 |
| work_keys_str_mv |
AT dengyangkendi weakandstrongestimatesforlinearandmultilinearfractionalhausdorffoperatorsontheheisenberggroup AT zhangxingsong weakandstrongestimatesforlinearandmultilinearfractionalhausdorffoperatorsontheheisenberggroup AT yandunyan weakandstrongestimatesforlinearandmultilinearfractionalhausdorffoperatorsontheheisenberggroup AT weimingquan weakandstrongestimatesforlinearandmultilinearfractionalhausdorffoperatorsontheheisenberggroup |
| _version_ |
1718371647683035136 |